Painleve Equations in the Differential Geometry of Surfaces: 1753 (Lecture Notes in Mathematics) - Tapa blanda

Bobenko, Alexander I.; Eitner, Ulrich

9783540414148: Painleve Equations in the Differential Geometry of Surfaces: 1753 (Lecture Notes in Mathematics)

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ISBN 10: 3540414142 ISBN 13: 9783540414148

Editorial: Springer, 2008

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Book by TU Berlin Alexander I Bobenko Eitner Ulrich

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Since the time of surfaces -+ in differential Gauss, parametrized (x, y) P(x, y) have been described a frame attached to the moving geometry through TI(x, y) surface. One introduces the Gauss- which linear dif- Weingarten equations are , ferential equations = U = TIX T1, VT', !PY (1. for the and their condition frame, compatibility - = V + [U, V] 0, UY (1.2) which the Gauss-Codazzi For surfaces in three-dim- represents equations . a sional Euclidean the frame T1 lies in the usually or space, group SO(3) SU(2). On the other a of a non-linear in the form hand, representation equation (1.2) is the of the of of starting point theory integrable equations (theory solitons), which in mathematical in the 1960's appeared physics [NMPZ, AbS, CD, FT, More the differential for the coefficients of AbC]. exactly, partial equation (1.2) the matrices U and V is considered to be if these matrices can be integrable , extended to U V non-trivially a one-parameter family (x, y, A), (x, y, A) satisfying - = + U(A)y V(A). [U(A), V(A)] 0, (1-3) so that the differential is and original partial equation preserved.' . Usually U(A) V are rational functions of the which is called the (A) parameter A, spectral param- In soliton the eter is called the Lax . theory, representation (1.3) representation the Zakharov-Shabat or representation [ZS].

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This book brings together two different branches of mathematics: the theory of Painlev� and the theory of surfaces. Self-contained introductions to both these fields are presented. It is shown how some classical problems in surface theory can be solved using the modern theory of Painlev� equations. In particular, an essential part of the book is devoted to Bonnet surfaces, i.e. to surfaces possessing families of isometries preserving the mean curvature function. A global classification of Bonnet surfaces is given using both ingredients of the theory of Painlev� equations: the theory of isomonodromic deformation and the Painlev� property. The book is illustrated by plots of surfaces. It is intended to be used by mathematicians and graduate students interested in differential geometry and Painlev� equations. Researchers working in one of these areas can become familiar with another relevant branch of mathematics.

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EditorialSpringer
A�o de publicaci�n2008
ISBN 10 3540414142
ISBN 13 9783540414148
Encuadernaci�nTapa blanda
IdiomaIngl�s
N�mero de p�ginas124

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Painlev� equations in the differential geometry of surfaces.

Bobenko, Alexander I.:

Publicado por Berlin, Springer, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces (Lecture Notes in Mathematics, 1753)

TU Berlin, Alexander I. Bobenko; Eitner, Ulrich

Publicado por Springer, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces

Bobenko, Alexander I.

Publicado por Springer 2000-12, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces (Lecture Notes in Mathematics, 1753)

TU Berlin, Alexander I. Bobenko; Eitner, Ulrich

Publicado por Springer, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces

Ulrich Eitner

Publicado por Springer Berlin Heidelberg Dez 2000, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Taschenbuch. Condici�n: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Since the time of surfaces -+ in differential Gauss, parametrized (x, y) P(x, y) have been described a frame attached to the moving geometry through TI(x, y) surface. One introduces the Gauss- which linear dif- Weingarten equations are , ferential equations = U = TIX T1, VT', !PY (1. for the and their condition frame, compatibility - = V + [U, V] 0, UY (1.2) which the Gauss-Codazzi For surfaces in three-dim- represents equations . a sional Euclidean the frame T1 lies in the usually or space, group SO(3) SU(2). On the other a of a non-linear in the form hand, representation equation (1.2) is the of the of of starting point theory integrable equations (theory solitons), which in mathematical in the 1960's appeared physics [NMPZ, AbS, CD, FT, More the differential for the coefficients of AbC]. exactly, partial equation (1.2) the matrices U and V is considered to be if these matrices can be integrable , extended to U V non-trivially a one-parameter family (x, y, A), (x, y, A) satisfying - = + U(A)y V(A). [U(A), V(A)] 0, (1-3) so that the differential is and original partial equation preserved.' . Usually U(A) V are rational functions of the which is called the (A) parameter A, spectral param- In soliton the eter is called the Lax . theory, representation (1.3) representation the Zakharov-Shabat or representation [ZS]. 128 pp. Englisch. N� de ref. del art�culo: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces

Ulrich Eitner Alexander I. Bobenko

Publicado por Springer, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Painleve Equations in the Differential Geometry of Surfaces

Ulrich Eitner

Publicado por Springer Berlin Heidelberg, 2000

ISBN 10: 3540414142 ISBN 13: 9783540414148

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Taschenbuch. Condici�n: Neu. Druck auf Anfrage Neuware - Printed after ordering - Since the time of surfaces -+ in differential Gauss, parametrized (x, y) P(x, y) have been described a frame attached to the moving geometry through TI(x, y) surface. One introduces the Gauss- which linear dif- Weingarten equations are , ferential equations = U = TIX T1, VT', !PY (1. for the and their condition frame, compatibility - = V + [U, V] 0, UY (1.2) which the Gauss-Codazzi For surfaces in three-dim- represents equations . a sional Euclidean the frame T1 lies in the usually or space, group SO(3) SU(2). On the other a of a non-linear in the form hand, representation equation (1.2) is the of the of of starting point theory integrable equations (theory solitons), which in mathematical in the 1960's appeared physics [NMPZ, AbS, CD, FT, More the differential for the coefficients of AbC]. exactly, partial equation (1.2) the matrices U and V is considered to be if these matrices can be integrable , extended to U V non-trivially a one-parameter family (x, y, A), (x, y, A) satisfying - = + U(A)y V(A). [U(A), V(A)] 0, (1-3) so that the differential is and original partial equation preserved.' . Usually U(A) V are rational functions of the which is called the (A) parameter A, spectral param- In soliton the eter is called the Lax . theory, representation (1.3) representation the Zakharov-Shabat or representation [ZS]. N� de ref. del art�culo: 9783540414148

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